You should take a serious look at Making Music Matter from Frank Ticheli. It starts the horns and saxes on “good” notes. Kids are playing chords from the first note, which requires the teacher to differentiate pitches. I think that’s the biggest drawback. It’s easier to hear the wrong notes when you’re playing unison, but it teaches independence from day 1.

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I've been using the Musical Mastery method book with my beginner saxophone class; before we left for covid-break, my beginner saxophones were way further ahead than usual!